%------------------------------------------------------------------------------ % File : Duper---1.0 % Problem : SEV259^5 : TPTP v9.2.0. Released v4.0.0. % Transfm : none % Format : tptp:raw % Command : duper %s % Computer : n005.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Fri Oct 3 08:03:00 PM UTC 2025 % Result : Theorem 4.01s 4.26s % Output : Proof 4.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEV259^5 : TPTP v9.2.0. Released v4.0.0. % 0.07/0.14 % Command : duper %s % 0.13/0.34 % Computer : n005.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.35 % WCLimit : 300 % 0.13/0.35 % DateTime : Fri Oct 3 01:46:23 EDT 2025 % 0.13/0.35 % CPUTime : % 4.01/4.26 SZS status Theorem for theBenchmark.p % 4.01/4.26 SZS output start Proof for theBenchmark.p % 4.01/4.26 Clause #0 (by assumption #[]): Eq % 4.01/4.26 (Not % 4.01/4.26 (∀ (S : (b → Prop) → Prop), % 4.01/4.26 And % 4.01/4.26 (And % 4.01/4.26 (And (∀ (R : b → Prop), (Eq R fun Xx => False) → S R) (∀ (R : b → Prop), (Eq R fun Xx => Not False) → S R)) % 4.01/4.26 (∀ (K : (b → Prop) → Prop) (R : b → Prop), % 4.01/4.26 And (∀ (Xx : b → Prop), K Xx → S Xx) (Eq R fun Xx => Exists fun S0 => And (K S0) (S0 Xx)) → S R)) % 4.01/4.26 (∀ (Y Z S0 : b → Prop), And (And (S Y) (S Z)) (Eq S0 fun Xx => And (Y Xx) (Z Xx)) → S S0) → % 4.01/4.26 ∀ (W : b → Prop) (Xx : b), % 4.01/4.26 W Xx → % 4.01/4.26 ∀ (S0 : b → Prop), % 4.01/4.26 And (∀ (Xx0 : b), W Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → S R) → S0 Xx)) % 4.01/4.26 True % 4.01/4.26 Clause #1 (by clausification #[0]): Eq % 4.01/4.26 (∀ (S : (b → Prop) → Prop), % 4.01/4.26 And % 4.01/4.26 (And (And (∀ (R : b → Prop), (Eq R fun Xx => False) → S R) (∀ (R : b → Prop), (Eq R fun Xx => Not False) → S R)) % 4.01/4.26 (∀ (K : (b → Prop) → Prop) (R : b → Prop), % 4.01/4.26 And (∀ (Xx : b → Prop), K Xx → S Xx) (Eq R fun Xx => Exists fun S0 => And (K S0) (S0 Xx)) → S R)) % 4.01/4.26 (∀ (Y Z S0 : b → Prop), And (And (S Y) (S Z)) (Eq S0 fun Xx => And (Y Xx) (Z Xx)) → S S0) → % 4.01/4.26 ∀ (W : b → Prop) (Xx : b), % 4.01/4.26 W Xx → % 4.01/4.26 ∀ (S0 : b → Prop), % 4.01/4.26 And (∀ (Xx0 : b), W Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → S R) → S0 Xx) % 4.01/4.26 False % 4.01/4.26 Clause #2 (by clausification #[1]): ∀ (a : (b → Prop) → Prop), % 4.01/4.26 Eq % 4.01/4.26 (Not % 4.01/4.26 (And % 4.01/4.26 (And % 4.01/4.26 (And (∀ (R : b → Prop), (Eq R fun Xx => False) → skS.0 0 a R) % 4.01/4.26 (∀ (R : b → Prop), (Eq R fun Xx => Not False) → skS.0 0 a R)) % 4.01/4.26 (∀ (K : (b → Prop) → Prop) (R : b → Prop), % 4.01/4.26 And (∀ (Xx : b → Prop), K Xx → skS.0 0 a Xx) (Eq R fun Xx => Exists fun S0 => And (K S0) (S0 Xx)) → % 4.01/4.26 skS.0 0 a R)) % 4.01/4.26 (∀ (Y Z S0 : b → Prop), % 4.01/4.26 And (And (skS.0 0 a Y) (skS.0 0 a Z)) (Eq S0 fun Xx => And (Y Xx) (Z Xx)) → skS.0 0 a S0) → % 4.01/4.26 ∀ (W : b → Prop) (Xx : b), % 4.01/4.26 W Xx → % 4.01/4.26 ∀ (S0 : b → Prop), % 4.01/4.26 And (∀ (Xx0 : b), W Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) → % 4.01/4.26 S0 Xx)) % 4.01/4.26 True % 4.01/4.26 Clause #3 (by clausification #[2]): ∀ (a : (b → Prop) → Prop), % 4.01/4.26 Eq % 4.01/4.26 (And % 4.01/4.26 (And % 4.01/4.26 (And (∀ (R : b → Prop), (Eq R fun Xx => False) → skS.0 0 a R) % 4.01/4.26 (∀ (R : b → Prop), (Eq R fun Xx => Not False) → skS.0 0 a R)) % 4.01/4.26 (∀ (K : (b → Prop) → Prop) (R : b → Prop), % 4.01/4.26 And (∀ (Xx : b → Prop), K Xx → skS.0 0 a Xx) (Eq R fun Xx => Exists fun S0 => And (K S0) (S0 Xx)) → % 4.01/4.26 skS.0 0 a R)) % 4.01/4.26 (∀ (Y Z S0 : b → Prop), % 4.01/4.26 And (And (skS.0 0 a Y) (skS.0 0 a Z)) (Eq S0 fun Xx => And (Y Xx) (Z Xx)) → skS.0 0 a S0) → % 4.01/4.26 ∀ (W : b → Prop) (Xx : b), % 4.01/4.26 W Xx → % 4.01/4.26 ∀ (S0 : b → Prop), % 4.01/4.26 And (∀ (Xx0 : b), W Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) → S0 Xx) % 4.01/4.26 False % 4.01/4.26 Clause #5 (by clausification #[3]): ∀ (a : (b → Prop) → Prop), % 4.01/4.26 Eq % 4.01/4.26 (∀ (W : b → Prop) (Xx : b), % 4.01/4.26 W Xx → % 4.01/4.26 ∀ (S0 : b → Prop), % 4.01/4.26 And (∀ (Xx0 : b), W Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) → S0 Xx) % 4.01/4.26 False % 4.01/4.26 Clause #15 (by clausification #[5]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop), % 4.01/4.26 Eq % 4.01/4.26 (Not % 4.01/4.26 (∀ (Xx : b), % 4.01/4.26 skS.0 1 a a_1 Xx → % 4.01/4.26 ∀ (S0 : b → Prop), % 4.01/4.26 And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → S0 Xx0) % 4.01/4.26 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) → % 4.01/4.26 S0 Xx)) % 4.01/4.26 True % 4.01/4.26 Clause #16 (by clausification #[15]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop), % 4.01/4.26 Eq % 4.01/4.26 (∀ (Xx : b), % 4.01/4.26 skS.0 1 a a_1 Xx → % 4.01/4.26 ∀ (S0 : b → Prop), % 4.11/4.28 And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → S0 Xx0) % 4.11/4.28 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) → % 4.11/4.28 S0 Xx) % 4.11/4.28 False % 4.11/4.28 Clause #17 (by clausification #[16]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b), % 4.11/4.28 Eq % 4.11/4.28 (Not % 4.11/4.28 (skS.0 1 a a_1 (skS.0 2 a a_1 a_2) → % 4.11/4.28 ∀ (S0 : b → Prop), % 4.11/4.28 And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → S0 Xx0) % 4.11/4.28 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) → % 4.11/4.28 S0 (skS.0 2 a a_1 a_2))) % 4.11/4.28 True % 4.11/4.28 Clause #18 (by clausification #[17]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b), % 4.11/4.28 Eq % 4.11/4.28 (skS.0 1 a a_1 (skS.0 2 a a_1 a_2) → % 4.11/4.28 ∀ (S0 : b → Prop), % 4.11/4.28 And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) → % 4.11/4.28 S0 (skS.0 2 a a_1 a_2)) % 4.11/4.28 False % 4.11/4.28 Clause #19 (by clausification #[18]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b), Eq (skS.0 1 a a_1 (skS.0 2 a a_1 a_2)) True % 4.11/4.28 Clause #20 (by clausification #[18]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b), % 4.11/4.28 Eq % 4.11/4.28 (∀ (S0 : b → Prop), % 4.11/4.28 And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → S0 Xx0) (∀ (R : b → Prop), (Eq R fun Xx0 => Not (S0 Xx0)) → skS.0 0 a R) → % 4.11/4.28 S0 (skS.0 2 a a_1 a_2)) % 4.11/4.28 False % 4.11/4.28 Clause #22 (by clausification #[20]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop), % 4.11/4.28 Eq % 4.11/4.28 (Not % 4.11/4.28 (And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → skS.0 3 a a_1 a_2 a_3 Xx0) % 4.11/4.28 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (skS.0 3 a a_1 a_2 a_3 Xx0)) → skS.0 0 a R) → % 4.11/4.28 skS.0 3 a a_1 a_2 a_3 (skS.0 2 a a_1 a_2))) % 4.11/4.28 True % 4.11/4.28 Clause #23 (by clausification #[22]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop), % 4.11/4.28 Eq % 4.11/4.28 (And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → skS.0 3 a a_1 a_2 a_3 Xx0) % 4.11/4.28 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (skS.0 3 a a_1 a_2 a_3 Xx0)) → skS.0 0 a R) → % 4.11/4.28 skS.0 3 a a_1 a_2 a_3 (skS.0 2 a a_1 a_2)) % 4.11/4.28 False % 4.11/4.28 Clause #24 (by clausification #[23]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop), % 4.11/4.28 Eq % 4.11/4.28 (And (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → skS.0 3 a a_1 a_2 a_3 Xx0) % 4.11/4.28 (∀ (R : b → Prop), (Eq R fun Xx0 => Not (skS.0 3 a a_1 a_2 a_3 Xx0)) → skS.0 0 a R)) % 4.11/4.28 True % 4.11/4.28 Clause #25 (by clausification #[23]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop), % 4.11/4.28 Eq (skS.0 3 a a_1 a_2 a_3 (skS.0 2 a a_1 a_2)) False % 4.11/4.28 Clause #27 (by clausification #[24]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop), % 4.11/4.28 Eq (∀ (Xx0 : b), skS.0 1 a a_1 Xx0 → skS.0 3 a a_1 a_2 a_3 Xx0) True % 4.11/4.28 Clause #32 (by clausification #[27]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 a_3 : b) (a_4 : b → Prop), % 4.11/4.28 Eq (skS.0 1 a a_1 a_2 → skS.0 3 a a_1 a_3 a_4 a_2) True % 4.11/4.28 Clause #33 (by clausification #[32]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 a_3 : b) (a_4 : b → Prop), % 4.11/4.28 Or (Eq (skS.0 1 a a_1 a_2) False) (Eq (skS.0 3 a a_1 a_3 a_4 a_2) True) % 4.11/4.28 Clause #34 (by superposition #[33, 19]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop) (a_4 : b), % 4.11/4.28 Or (Eq (skS.0 3 (fun x => a x) (fun x => a_1 x) a_2 a_3 (skS.0 2 a a_1 a_4)) True) (Eq False True) % 4.11/4.28 Clause #97 (by betaEtaReduce #[34]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop) (a_4 : b), % 4.11/4.28 Or (Eq (skS.0 3 a a_1 a_2 a_3 (skS.0 2 a a_1 a_4)) True) (Eq False True) % 4.11/4.28 Clause #98 (by clausification #[97]): ∀ (a : (b → Prop) → Prop) (a_1 : b → Prop) (a_2 : b) (a_3 : b → Prop) (a_4 : b), % 4.11/4.28 Eq (skS.0 3 a a_1 a_2 a_3 (skS.0 2 a a_1 a_4)) True % 4.11/4.28 Clause #99 (by superposition #[98, 25]): Eq True False % 4.11/4.28 Clause #103 (by clausification #[99]): False % 4.11/4.28 SZS output end Proof for theBenchmark.p %------------------------------------------------------------------------------